Subgroups — #16854109

Order 3968.

648 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758446	C₂	1	6	yes	maximal
2	#14520919	C₂	1	8	yes	maximal
3	C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₆₂	C₂²	1	4	yes	—
5	C₂×C₄²×C₃₁	C₂²	1	3	yes	—
6	C₂×C₄²×C₃₁	C₂²	1	4	yes	—
7	C₂×C₄⋊Dic₃₁	C₂²	1	24	yes	—
8	#11758446	—	2	24	no	—
9	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₃₁	C₂³	1	6	yes	—
11	C₂²×Dic₃₁	C₂³	1	8	yes	—
12	C₂×Dic₆₂	—	2	24	no	—
13	C₄²×C₃₁	D₄	1	12	yes	—
14	C₄²×C₃₁	Q₈	1	16	yes	complemented
15	C₄⋊Dic₃₁	—	2	48	no	—
16	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
17	C₂×C₄×C₃₁	C₂×D₄	1	6	yes	—
18	C₂×C₄×C₃₁	C₂×D₄	1	12	yes	—
19	C₂×C₄×C₃₁	C₂×Q₈	1	24	yes	—
20	C₂×Dic₃₁	—	2	24	no	—
21	Dic₆₂	—	4	16	no	—
22	#2868	—	31	1	no	maximal, Sylow
23	C₂²×C₃₁	C₂²×D₄	1	3	yes	—
24	C₂²×C₃₁	C₂²×Q₈	1	4	yes	—
25	C₄×C₃₁	#127	1	4	yes	—
26	C₄×C₃₁	C₄⋊Q₈	1	24	yes	complemented
27	Dic₃₁	—	4	8	no	—
28	C₂×C₄⋊Q₈	—	31	6	no	—
29	#384	—	31	8	no	—
30	C₄³	D₃₁	1	1	yes	characteristic
31	C₂×C₃₁	C₂×#127	1	1	yes	characteristic
32	C₂×C₃₁	C₂×C₄⋊Q₈	1	6	yes	—
33	C₂²×Q₈	—	31	4	no	—
34	C₄⋊Q₈	—	62	24	no	—
35	C₂×C₄⋊C₄	—	31	24	no	—
36	C₂×C₄²	C₂×D₃₁	1	4	yes	—
37	C₂×C₄²	C₂×D₃₁	1	3	yes	—
38	C₃₁	#2868	1	1	yes	characteristic, complemented, Sylow
39	C₂×Q₈	—	62	24	no	—
40	C₂²×C₄	—	31	8	no	—
41	C₂²×C₄	C₂²×D₃₁	1	6	yes	—
42	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
43	C₄⋊C₄	—	62	48	no	—
44	C₄²	Dic₆₂	1	16	yes	complemented
45	C₄²	D₁₂₄	1	12	yes	—
46	C₂³	C₂³×D₃₁	1	1	yes	characteristic
47	Q₈	—	124	16	no	—
48	C₂×C₄	—	62	24	no	—
49	C₂×C₄	C₂×Dic₆₂	1	24	yes	—
50	C₂×C₄	C₂×D₁₂₄	1	12	yes	—
51	C₂×C₄	C₂×D₁₂₄	1	6	yes	—
52	C₂²	C₂²×Dic₆₂	1	4	yes	—
53	C₂²	C₂²×D₁₂₄	1	3	yes	—
54	C₄	—	124	8	no	—
55	C₄	#11758446	1	24	yes	complemented
56	C₄	#11758451	1	4	yes	—
57	C₂	C₂×#11758451	1	1	yes	characteristic
58	C₂	C₂×#11758446	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₃₁
commutator, socle, prime radical, cosocle	C₂³×C₃₁	C₂⁴
Fitting	C₄³×C₃₁	C₂
hypercenter	C₄³	D₃₁
hypocenter	C₃₁	#2868
LCS	G ▷ C₂³×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
14. C₄²×C₃₁	Q₈	semidirect
26. C₄×C₃₁	C₄⋊Q₈	semidirect
38. C₃₁	#2868	semidirect
44. C₄²	Dic₆₂	semidirect
55. C₄	#11758446	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11758446	2
#14520919	2
C₄³×C₃₁	2
#2868	31